On the Use of a Regret Function to Set Significance Points in Prior Tests of Estimation

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Abstract
In linear models, an F-test may be used to decide on restricted or unrestricted estimators. To avoid the arbitrariness of the significance level and undesirable quadratic risk properties, a regret criterion is proposed, extending the results of Sawa and Hiromatsu [4]. Optimal critical points of the prior F-test and their corresponding significance levels are tabulated for different sample sizes and number of restrictions. The critical value is generally close to two, but much smaller if the columns of the design matrix are nonorthogonal. This suggests that if the F-statistic is more than two, the unrestricted estimator should be used.

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